Multigrid Geometric Active Contours

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Overview

Geometric active contour/snake models are very popular partial differential
equation-based tools in image analysis and computer vision, with numerous
applications such as image segmentation and moving object tracking. These
models are conveniently implemented with level sets, but traditional
level-set-based implementations have been notoriously slow.

We have developed novel multigrid algorithms for the fast evolution of
level-set-based geometric active contours, which allow real-time performance
on conventional PCs. We overcome the main bottleneck associated with most
numerical implementations of geometric active contours, namely the need for
very small time steps to avoid instability, by employing a very stable fully
2-D implicit-explicit time integration numerical scheme. The proposed scheme
is more accurate and has improved rotational invariance properties compared
with alternative split schemes, particularly when big time steps are
utilized. We then apply properly designed multigrid methods to efficiently
solve the occurring sparse linear system. The combined algorithm allows for
the rapid evolution of the contour and convergence to its final configuration
after very few iterations.

Key for the efficiency of the technique is the solution of a big sparse linear
system with multigrid techniques, which attack the problem at
multiple resolutions, in one of the schedules depicted on Figure 2: